Tensor Algebras overC*-Correspondences: Representations, Dilations, andC*-Envelopes
✍ Scribed by Paul S. Muhly; Baruch Solel
- Book ID
- 102972593
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 665 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
Tensor algebras over C*-correspondences are noncommutative generalizations of the disk algebra. They contain, as special cases, analytic crossed products, semicrossed products, and Popescu's noncommutative disk algebras. In this paper, a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved. These are used to show that for certain C*-correspondences, the C*-envelopes (in the sense of Arveson) of the tensor algebras are the Cuntz Pimsner algebras of the correspondences.
1998 Academic Press classical dilation theory which, in turn, has been a central theme in operator theory for over 40 years. If A is an operator algebra, then its C*-envelope, C*(A), is a C*-algebra containing (a copy of ) A that is essentially uniquely determined by the requirement that the so-called Shilov boundary ideal article no. FU983294